Caseyev teorem

• Main Author: Naglaš, Adam
• Other Authors: Bombardelli, Mea
• Format: Master Thesis
• Language: Croatian
• Published: Sveučilište u Zagrebu. Prirodoslovno-matematički fakultet. Matematički odsjek. 2019
• Subjects: Caseyev teorem; Ptolomejev teorem; geometrijski zadaci; inverzija; Casey’s theorem; Ptolemy’s theorem; geometric problems; inversion; PRIRODNE ZNANOSTI. Matematika; NATURAL SCIENCES. Mathematics; sami
• Online Access: https://zir.nsk.hr/islandora/object/pmf:6184; https://urn.nsk.hr/urn:nbn:hr:217:920742; https://repozitorij.unizg.hr/islandora/object/pmf:6184; https://repozitorij.unizg.hr/islandora/object/pmf:6184/datastream/PDF

U ovom diplomskom radu bavimo se Caseyevim teoremom. U prvom poglavlju iskazujemo i dokazujemo Ptolomejev teorem kako bismo pobliže razumjeli Caseyev teorem, te definiramo osnovne pojmove koje koristimo kroz rad. U drugom poglavlju pažnju posvećujemo inverziji koja se koristi u dokazivanju Caseyevog teorema. U trećem poglavlju iskazujemo i dokazujemo Caseyev teorem na nekoliko načina i dokazujemo specijalne slučajeve Caseyevog teorema. Sami kraj rada posvećen je primjeni Caseyevog teorema u dokazivanju drugih teorema i u rješavanju geometrijskih zadataka. In this graduate thesis we are dealing with Casey’s theorem. In the first chapter, we formulate and prove Ptolemy’s theorem to better understand Casey’s theorem, and define the basic terms we use through graduate thesis. In the second chapter, we dedicate to the inversion used to prove Casey’s theorem. In the third chapter, we phrase and prove Casey’s theorem in several ways and prove the special cases of Casey’s theorem. The end of the graduate thesis is dedicated to the application of Casey’s theorem in proving other theorems and in solving geometric problems.